The fraction of the sky over which an adaptive-optics (AO) system will provide a useful level of performance is limited by anisoplanatism. One measure of sky coverage is the probabilty P(P ≥ S*) that the system will provide a Strehl ratio S no smaller than a threshold value S* when observing in a random direction selected without reference to the distribution of guide stars. This probability is a function of the atmospheric turbulence and wind velocity profiles, the telescope aperture diameter, the observing wavelength, the density of guide stars as a function of magnitude, and the characteristics of the adaptive-optics system. Some of these characteristics include the photon efficiency of the wavefront sensor (WFS), the order and efficiency of the AO correction, and bandwidth of the AO control loop. The values of these parameters which will maximize P(P ≥ S*) for a natural guide star (NGS) AO system are strongly dependant upon the choice of the threshold Strehl ratio S*, while current interest in laser guide star (LGS) adaptive-optics is of course motivated by the potential for dramatic increases in P(S > S*) for large values of S* at visible and near infrared wavelengths.